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divisibility

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divisibility

by vaivish » Sun Jan 17, 2010 10:06 am
If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what
is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.

OA is c.

pl explain.
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Source: — Data Sufficiency |
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by linkinpark » Mon Jan 18, 2010 9:08 am
vaivish wrote:If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what
is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.

OA is c.

pl explain.
1) consider n = 5, 7 then n^2 - 1 leaves remainder 0, now consider n=9 => n^2 - 1 = 81-1=80 so 80/24 will leave 8 as remainder. so not sufficient to determine

2) consider n=5,7 again we'll get same r=0, now consider n=8, n^2 - 1 = 63, 63/24 will give remainder 15 so we can't determine.

now combining 1 & 2, we get only limited numbers like 5,7,11 which leave r=0 so together they're sufficient. only prime numbers [>3] satisfy the equation.
530->480->580
when posting a question don't post OA(even masked) before some discussion.
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